Question

A particle is moving on the x-axis. Its position is given by x = 2t^2 - 12t + 4 for times t ≥ 0

Answer 1

a) - 10 m/s

b) 10 m/s

c) - 10 m/s²

Explanation:

Given, a particle moving on the x-axis. Its position is:

• x = 2t^2 - 12t + 4, t ≥ 0

Let's assume unit of x is m.

For t= 0,

• x = 0 - 0 + 4 = 4 m

For t = 1,

• x = 2*1^2 - 12*1 + 4 = 2 - 12 + 4 = - 6 m

a) Velocity at time t=1

Velocity = displacement/time = (-6- 4)/1 = - 10 m/s as it moves to the left

b) Speed at time t = 1

Speed = distance/time = (4 + |6|)/1 = 10 m/s

c) Acceleration at t = 1

Acceleration is rate of change of velocity.

It took 1 sec to change velocity from 0 to - 10 m/s

So acceleration is:

• -10 m/s / 1 s = -10 m/s²