| The distance travelled by a body moving along a line in time / is proportional to t3. |
| The acceleration-time (a, t) graph for the motion of the body will be [JEE ONLINE 12-05-2012] |
A)
B)
C)
D)
Correct Answer: B
Solution :
| [b] Distance along a line i.e., displacement (s) |
| \[={{t}^{3}}(\because s\propto {{t}^{3}}\,\text{given})\] |
| By double differentiation of displacement, we get acceleration. |
| \[V=\frac{ds}{dt}=\frac{d{{t}^{3}}}{dt}=3{{t}^{2}}\] and \[a=\frac{dv}{dt}=\frac{d3{{t}^{3}}}{dt}=6t\] |
| \[a=6t\]or\[a\propto t\] |
| Hence graph [b] is correct. |
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