Question Detail
Question
The motion of a particle along a straight line is specified by the equation x = 4t4 – 3t3, find the acceleration after 3 seconds.
Correct Answer
Option B is the correct answer.
Detailed Explanation
- Find the velocity (v) by differentiating x with respect to t: x = 4t4 - 3t3 v = dx/dt = 16t3 - 9t22. Find the acceleration (a) by differentiating v with respect to t: a = dv/dt = d/dt (16t3 - 9t2) = 48t2 - 18t3. Evaluate the acceleration at t = 3 seconds: a(3) = 48(3)2 - 18(3) a(3) = 48(9) - 54 a(3) = 432 - 54 a(3) = 378 ms-2.Note: Option B has 'ms' as the unit, which is a typo and should be 'ms-2'. However, the numerical value 378 is correct.
Hint
Acceleration is the second derivative of position with respect to time. Differentiate twice and then substitute t=3.