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.

A boy is moving with constant velocity 10 m//s. A car starts from rest

1.	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.
Answer» Solution : 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)