Question

A point initially at rest moves along x-axis. It's acceleration varies with time as a=(6t+5)m/s^2. If it starts from origin, the distance covered in 2s is : ? ​

Answer 1

a = 6t + 5

dv/dt = 6t + 5, on integrating

v = 3t^2 + 5t

ds/dt = 3t^2 + 5t , again on integrating

it starts from origin so limits are 0 to S in 0 to 2 sec

S = (t^3 + 2.5t^2) limit 0 to 2

S = 18m