Question

if displacement of a particle is given by s=2t^2 +4t where t = time, find the velocity and acceleration at t=2 seconds.

Answer 1

Displacement of particle (s) = $2t^2 + 4t$

Velocity (v) = $\frac{\delta s}{\delta t}$

$\frac{\delta s}{\delta t}$ = 4t + 4

Hence, at t = 2:

Velocity = 4 × 2 + 4 = 8 + 4

Velocity (v) = 12 m/s

Hence, the velocity of the particle is 12 m/s at t = 2 seconds.

Now,

a = $\frac{\delta v}{\delta t}$

$\frac{\delta v}{\delta t}$ = 4 m/s^2

Hence, at t = 2 seconds:

Acceleration (a) = 4 m/s^2