Question

The displacement(in metres) of a particle moving along x-axis is given by x=18t+5t^2.Calculate: i)instantaneous velocity at t=2s ii)instantaneous acceleration.

Answer 1

instantaneous velocity(v)=dx/dt=18+10t
thus v at t=2s=18+10×2=38m/s
instantaneous accelaration=dv/dt=10m/s^2

Answer 2

i)
x = 18t + 5t^2
v = 18 + 10t
At t = 2s
v = 18 + 10*2
v = 38 m/s
Instantaneous velocity at t = 2s is 38 m/s

ii)
v = 18 + 10t
a = 10 m/s^2
Instantaneous acceleration is 10 m/s^2