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    1. A car is waiting at traffic lights with a van behind it. There is a 1 metre gap between them. When the lights turn green, the car accelerates at 1.5 m/s until it reaches a speed of 15 m/s; it then proceeds at this speed. The van does the same, starting when the gap between the vehicles is 4 metres.Find a formula for the distance travelled by the car in the first t seconds (0<=t<=10), and hence the time interval between the car starting and the van starting. Find also the distance between the vehicles when they are both going at 15m/s.


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    (Original post by zt9028)
    1. A car is waiting at traffic lights with a van behind it. There is a 1 metre gap between them. When the lights turn green, the car accelerates at 1.5 m/s until it reaches a speed of 15 m/s; it then proceeds at this speed. The van does the same, starting when the gap between the vehicles is 4 metres.Find a formula for the distance travelled by the car in the first t seconds (0<=t<=10), and hence the time interval between the car starting and the van starting. Find also the distance between the vehicles when they are both going at 15m/s.


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    There is an equation relating displacement, time, initial velocity and acceleration. Using the formula you can find the time interval between the car and the van starting since you know the distance the car has travelled before the van started accelerating.

    For the last part, you need to find the gap between the car and the van when they have reached the speed of 15m/s, but because they accelerated at the same rate the distance between them should be the same as the distance the car has travelled to reach a speed of 15m/s, using v2=u2+2as, plus the initial gap between the vehicles before the van started accelerating as the car wouldn't travelled faster for the distance between them to increase.
 
 
 
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