On the Move Linear Motion

Speed and Velocity What is the difference between speed and velocity? Speed is a scalar Velocity is a vector (it involves a direction)

Speed and Velocity If an athlete runs 100 m in 10 s his average speed is 10m in 1 second or 10m/s. A speedometer of a car would not read 10m/s all the time,that is why we state the average speed.

Speed and Velocity Since the S.I. units for distance (length) are metres, and the S.I. units for time are seconds, the units for speed are metres per second (m/s).

Velocity Example Example 1: A car travels 100m in 5seconds, what is its average speed?

Example 2 A cheetah runs 300 metres in 20 seconds. What is the speed of the cheetah?

Distance-Time Graphs Distance-time graphs are graphs that when plotted, the distance travelled is on the y-axis, and the time taken is on the x-axis. A horizontal straight line in a distance-time graph, tells us that there is no motion. A straight slanting line in a distance-time graph, tells us that there is constant speed. The steeper the slope the greater the velocity. A curved line tells us that there is acceleration. No motion Constant velocity Acceleration

Distance-time Graph Constant Velocity in the opposite direction Distance/m Constant Velocity in the opposite direction Time / s

Finding Velocity in a Distance-Time Graph The velocity can be found using a distance-time graph from its gradient. Consider the graph below: One can find the gradient of this graph by taking any two points on the graph. For instance (1, 3) and (5, 15) Then put these co-ordinates in the formula: Note: When the distance-time graph is a horizontal line, it means that the gradient is zero. This means that there is no velocity (motion). Therefore the body is at rest. http://www.passmyexams.co.uk/GCSE/physics/speed_velocity.html#1

Acceleration If a car driver presses the accelerator, the car goes faster. We say that the car accelerates. Acceleration occurs when there is a change in velocity. Acceleration is the change of velocity (speed) per unit time. The units of acceleration are metres per second squared (m/s2) Note:- When we say that an object is at REST, it means that the object is not moving. So the speed/velocity of the object is 0 m/s.

Acceleration Example A train starts from rest, and it starts to accelerate. It reaches a velocity of 2 m/s after 1 second, what is the acceleration?

Deceleration Deceleration is the opposite of acceleration (negative acceleration). It is sometimes called retardation. Deceleration is for example, when we use the brakes to stop a car. The only difference is that when a car decelerates by 8 m/s2, we have to write -8 m/s2, and work out everything usual. So when there is deceleration, we have to write the minus sign (-) in front of the number.

Deceleration Example A car is travelling at 20m/s. The driver brakes constantly until the car stops. This takes 2 seconds, for the car to stop. Find the deceleration of the car.

VELOCITY-TIME (V-T) GRAPHS Velocity-time graphs are graphs that when plotted have the velocity on the y-axis, and the time taken on the x-axis. A horizontal straight line in a velocity-time graph tells that there is constant velocity or speed. A slope going upwards tells us that there was acceleration. The steeper the slope the greater the acceleration. A slope going downwards tells us that there was a deceleration. Constant velocity Acceleration Deceleration

Finding the acceleration and the distance from a velocity-time graph The acceleration or deceleration can be found in a v-t graph from the gradient of the graph. The distance travelled can also be found in a v-t graph by finding the area under the graph. Consider the velocity-time graph below: A B C D

Finding the acceleration and the distance from a velocity-time graph To find the acceleration of part A one has to find the gradient of the graph in part A Let’s condsider co-ordinates (1,2) and (2, 4) A B C D

Finding the acceleration and the distance from a velocity-time graph A B C D This procedure can be done for every part of the graph. In part B the gradient is O therefore one can notice that there is no acceleration, and therefore constant velocity takes place. To find the distance travelled in all parts one has to work out the area under the whole graph. Area in part A = Area of a triangle = ½ (4 x 8) = 16m Area in part B = Area of quadrilateral = 2 x 8 = 16m Area in part C = Area of a trapezium = ½ (20 + 8) X 4 = 56m Area in part D = Area of a triangle = ½ (4 x 20) = 40 m Distance covered = Total area under the graph = 128 m

Equations of motion The following are the 4 equations of motion: v = u + at v2=u2+2as s = ut+½at2 We write the equations of motion using the following 5 letters/symbols: s = distance travelled (m) u = initial velocity (m/s) v = final velocity (m/s) a = acceleration (m/s2) t = time taken (s) To remember all these letters we learn the word SUVAT

Working Problems A sports car accelerates from rest at 4m/s2 for 10 seconds. Calculate the final velocity. s u = 0 m/s v = ? a = 4m/s2 t = 10s

Working Problems 2. A lion starts from rest, and reaches a final velocity of 10m/s in 20 s. What is the distance travelled by the lion during this time? s = ? u = 0 m/s v = 10 m/s a = t = 20s

Working Problems 3. An athlete accelerates with the rate of 2m/s2 the 100m race from rest. At what velocity does he arrive at the finish line? s = 100 m u = 0 m/s v = ? a = 2 m/s2 t =

Working Problems 4. A car accelerates 2m/s2 from rest in 10 seconds. Find the distance travelled during the time of acceleration. s = ? u = 0 m/s v = a = 2m/s2 t = 10s