A boy is moving with constant velocity `10 m//s`. A car starts from rest as the boy passes and accelerates at `5 m//s^(2)`. After how much time and at what distance the car meets the boy? Sketch v-t and s-t graphs for the boy and car.

Explanation

Let the car meets the boy after time t and at distance d.
Boy: `d=v_(0)t=10 t …(i)`
Car: `s=ut+1/2 at^(2)`
`d=1/2.5t^(2)=5/2 t^(2) …(ii)`
`10 t=5/2 t^(2)impliest=4 s`
`d=10 t=40 m`
Boy: `v=v_(0)=10 m//s`
Shape: `y=10`, a straight line parallel to the t-axis
Car: `v=u+at=0+5 t`, at `t=4 s`, `v=20 m//s`
Shape: `y=5x`, Straight line, slope +ve

s-t graph
Boy: `s=v_(0)t=10 t, t=4 s, s=40 m`
Slope: `y=10x`, an inclined straight line of +ve slope
Car: `s=ut+1/2 at^(2)=1/2xx5xxt^(2), t=4 s, s=40 m`
Slope: `y=5/2x^(2)` (parabola, open upward)