Question

A truck traveling at a constant speed of 28 m/s passes a more slowly moving car. The instant the truck passes the car, the car begins to accelerate at a constant rate of 1.2 m/s^2 and passes the truck 545 m farther down the road. What was the speed of the car (in meters/second) when it was first passed by the truck?

Answer 1

As per the question asked the car passes the truck 545m with an acceleration of 1.2m/s^2 further down the road .So the car has covered a distance of 545m before it passed the truck.

By using newtons equations of motion for distance formula, S=ut+0.5at^2

where u is velocity of car when truck passed the car

   t is time taken by the car to pass the truck

   a is acceleration of the car =1.2m/s^2

S is the distance covered by the car to pass the truck

   ^

here time taken by the car to cover 545metres is equal to the time taken by the truck to travel 545 metres.as the truck is moving at constant speed we can find taken taken by truck to travel 545 metres which is given by   

T=Distance/speed

T=545/28=19.464 second

   so               

545=U(19.464)+0.5(1.2)(19.464)^@

545=U(19.464)+227.308

U(19.464)=545-227.308

U(19.464)=317.691

   U=317.691/19.464

   U=16.322 m/s