Question

The displacement of particle is
x = 10t + 15t^3
Find the velocity at t= 0 and acceleration
at t = 2s​

Answer 1

Answer:

velocity at t= 0 = 10 m/s

acceleration at t = 2s​ = 180 m/s^2

Explanation:

$\text{displacement, x = } 10t+15t^3\\ \\ \text{velocity,}\ \frac{dx}{dt} = \frac{d}{dt} \big(10t+15t^3\big) = 10+45t^2\\ \\ \text{at t=0, velocity,}\ v = 10+45 \times 0^2 = 10\ \text{m/s}$

$\text{acceleration,}\ \frac{dv}{dt} = \frac{d}{dt} \big(10+45t^2\big) =90t \\ \\ \text{at t=2, acceleration,}\ a = 90 \times 2 = 180\ m/s^2$

Answer 2

Acceleration of particle = 0 m/s²

for further explanation Refer the above attachment