Question

A car is moving in such a way that the distance it covers, is given by the equation s = 4t² + 3t, where s is in meters and t is in seconds. What would be the velocity and the acceleration of the car at time t = 20 seconds?

Answer 1

Let v be the velocity and a be the acceleration of the car.

Distance travelled by the car is given by

∴ Velocity = v = `("ds")/("dt")`

= `"d"/("dt")(4"t"^2 + 3"t")`

= 8t + 3   .......(i)

Acceleration = a = `("dv")/("dt")`

= `"d"/("dt")(8"t" + 3)`

= 8        .......(ii)

Velocity of the car at t = 20 seconds is

`"V"_(("t" = 20))` = 8(20) + 3      .......[From (i)]

= 163 m/sec.

Acceleration of the car at t = 20 seconds is

`"a"_(("t" = 20))` = 8 m/sec²    .......[From (ii)]