Question

A car starts from rest with acceleration $a=6t (ms^{-2})$. Its velocity and displacement after 4 seconds are ________.

• A. 48, 64
• B. 16, 24
• C. 16, 38
• D. 24, 32
• E. 32, 24

Hint:

$v = \int a dt$ and $s = \int v dt$.

Answer 1

The Correct Option is A

Step 1: Concept
Velocity is the integral of acceleration, and displacement is the integral of velocity.

Step 2: Meaning
$v = \int 6t dt = 3t^2$. $s = \int 3t^2 dt = t^3$.

Step 3: Analysis
At $t=4$: $v = 3(4^2) = 48 ms^{-1}$. $s = 4^3 = 64 m$.

Step 4: Conclusion
Velocity is 48 and displacement is 64. Final Answer: (A)