Cambridge International AS and A level Physics
a How can you tell from the graph that the vehicle started from rest? b After what time did the vehicle stop accelerating? Explain how you can tell. c The vehicle is accelerating in the section AB. Use the triangle ABX to calculate the time for which the vehicle accelerated in this section. d Deduce the increase in the vehicle’s velocity in this time. e Use your answers to c and d to calculate the vehicle’s acceleration in the section AB. f
Now consider section BC of the graph. Follow the same steps as parts c to e to calculate the vehicle’s acceleration in the section BC.
g Calculate the area of the triangle ABX. What does this area represent? h Calculate the total distance travelled by the vehicle in its journey ABCD. 2 This table shows how the velocity of a car changed as it moved along a straight road: Velocity / m s −1
10
10
17
24
28
28
28
0
20
40
60
80
100
120
Time / s
a Draw a velocity–time graph to represent the car’s journey. b Between which two times was the car’s acceleration greatest? Calculate its acceleration between these times. c Calculate the distance travelled by the car during its journey. You will need to divide the area under the graph into rectangles and triangles.
8
3 A car is approaching traffic lights. The driver brakes so that the car’s velocity decreases from 22 m s −1 to 7 m s −1 in a time of 10 s. a Sketch a velocity–time graph to represent this section of the car’s journey. b Calculate the car’s acceleration. c State how the graph shows that the car is decelerating. Remember that ‘decelerating’ means that the car’s velocity is decreasing; its acceleration is negative. d On your graph, shade the area which represents the car’s displacement as it is braking. e Calculate the displacement of the car as it is braking. 4 A moving train decelerates at a rate of 0.2 m s −2 for a time of 50 s. In this time it travels a distance of 2000 m. Deduce the train’s velocity just before it started to decelerate. Start by sketching a velocity–time graph and mark on it the information given in the question.
Exercise 2.2 Deriving the equations of motion There are four equations of motion, sometimes known as the ‘suvat equations’. This exercise will help you to understand their derivation. Equation 1:
v = u + at
Equation 2:
s=
Equation 3:
s = ut + 21 at 2
Equation 4:
v2 = u2 + 2as
(u + v ) × t 2
1 a Which quantities do the symbols s, u, v, a and t represent? b The equations only apply to an object moving with uniform acceleration in a straight line. What is meant by the phrase ‘uniform acceleration’? Remember that acceleration is a vector quantity.