Question

a particle moves with acceleration a equals 4t+2 m/s2.Find its displacement at t=4 sec if at origin its velocity was2m/s at start of motion​

Answer 1

Answer:

200/3 = 66.67 m is the required answer.

SOLUTION:

Refer to the attachment.

KEYS:

• Differentiation of displacement gives instantaneous velocity.

v = dx/dt

• Differentiation of velocity gives instantaneous acceleration.

a = dv/dt

• Integration of acceleration gives the change in velocity over a particular interval of time.

• Integration of velocity gives the displacement over a particular interval of time.

SOLUTION STEPS:

1. Integrating acceleration of 4t + 2 m/s² gives the change in velocity.

2. Since the initial velocity is 2 m/s , the final velocity becomes , v = 2 ( t² + t + 1 ) m/s

3. Integrate the velocity to get the required displacement equation.

4. Substitute t = 4 sec in the equation

x = 2 ( t³/3 + t²/2 + t ) m

5. We get the required answer as 200/3 m

6. The displacement at t = 4 sec is 66.67 m

Answer 2

Answer:

the answer of your question is 152 m