Cambridge International AS and A level Physics
d The area of a triangle = 12 × base × height. Use your answer from c to write down the area of the triangle in terms of a and t. e Write down the complete equation for displacement s in terms of the two areas. f
Which of the five quantities from question 1 is not involved in this equation?
5 Equation 4 has to be deduced from the equations 1 and 2, using algebra. a Write out equation 1. Rearrange it so that time t is its subject. b Write out equation 2. Substitute for t using your answer to part a. c Rearrange the equation to give an expression which has the form of ‘the difference of two squares’. d Make v2 the subject of the equation. e Which of the five quantities from question 1 is not involved in this equation?
Exercise 2.3 Using the equations of motion When using the equations of motion, you need to identify the ‘suvat’ quantities involved and the equation that links them. 1 A truck is moving at 12 m s −1. It accelerates uniformly at 0.75 m s −2 for 20 s. a Calculate the velocity of the truck after this time. b Calculate the average velocity of the truck while it is accelerating. c Use your answers to a and b to calculate the distance the lorry travels while it is accelerating.
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d Check that you get the same answer to c using the equation: TIP Because the four suvat equations are connected to each other, you can usually find a way of using an alternative equation to check an answer.
s = ut 21 + at 2 2 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. Use one of the equations of motion to deduce the train’s velocity just before it started to accelerate. (This is question 4 from Exercise 2.1 but now you can solve it more directly using one of the equations of motion.) 3 A car is stationary. It accelerates at 0.8 m s −2 for 10 s and then at 0.4 m s −2 for a further 10 s. Use the equations of motion to deduce the car’s final displacement. You will have to split the journey into two parts, since the acceleration changes after 10 s. 4 A car is being tested on a track. The driver approaches the test section at a speed of 28 m s −1. He then accelerates at a uniform rate between two markers separated by 100 m. The car reaches a speed of 41 m s −1. a Calculate the car’s acceleration. b Calculate the time during which the car is accelerating.