Acceleration-time graphs Quiz 1

Question 1

Refer the $$a-t$$ graph below, determine the velocity at $$t=8	ext{ sec}$$ if $$v\left( 0 ight)=0$$.Also tell if the body is accelerating or decelerating? <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/d871b828-865d-43dd-9438-5ae4bf7fbacd4267735383890199268.png"/>

Accepted Answer

$$15	ext{ m}{{	ext{s}}^{-1}}	ext{ , accelerating}$$

Answer

$$16	ext{ m}{{	ext{s}}^{-1}}	ext{ , accelerating}$$

Answer

$$16	ext{ m}{{	ext{s}}^{-1}}	ext{ , decelerating}$$

Answer

$$15	ext{ m}{{	ext{s}}^{-1}}	ext{ , decelerating}$$

Question 2

Referring to the $$a-t$$ diagram given below, determine the change in velocity.<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/150c6459-f247-4fc8-93b7-ad0e7fbed9a25345123719888207136.png"/>

Accepted Answer

$$35	ext{ m}{{	ext{s}}^{-1}}$$

Answer

$$36	ext{ m}{{	ext{s}}^{-1}}$$

Answer

$$34	ext{ m}{{	ext{s}}^{-1}}$$

Answer

None of the above.

Question 3

A ball is moving in the positive $$X$$ direction such that $$x\left( t ight)=\left( 4{{t}^{3}}-2t+2 ight)	ext{ m}$$ . What is the acceleration time relationship, also find the change in acceleration for $$t=3	ext{ sec}$$ to $$t=6	ext{ sec}$$.

Accepted Answer

$$a=24t	ext{ , }72	ext{ m}{{	ext{s}}^{-2}}$$

Answer

$$a=62t	ext{ , 23 m}{{	ext{s}}^{-2}}$$

Answer

$$a=72t	ext{ , 24 m}{{	ext{s}}^{-2}}$$

Answer

$$a=23t	ext{ , 6}2	ext{ m}{{	ext{s}}^{-2}}$$

Question 4

A body of mass $$m$$ initially at rest is accelerating with respect to time as given: $$a\left( t ight)=\left( 4t-8 ight)	ext{ m}{{	ext{s}}^{-2}}$$. After travelling for $$3	ext{ sec}$$ it collides with a ball, finding the impulse delivered to the ball by the wall.

Accepted Answer

$$-6m	ext{ Ns}$$

Answer

$$-4m	ext{ Ns}$$

Answer

$$6m	ext{ Ns}$$

Answer

$$4m	ext{ Ns}$$

Question 5

If a small mass $$m$$ is accelerated by an acceleration of $$a\left( t ight)=\left( 2{{t}^{3}}-4{{t}^{2}}-t +1 ight)	ext{ m}{{	ext{s}}^{-2}}$$. Calculate the change in momentum for $$8	ext{ sec}$$ and the nature of the motion.

Accepted Answer

$$1000m	ext{ , accelerated motion with increasing acceleration after }t=\dfrac{8+\sqrt{40}}{12}	ext{.}$$

Answer

$$1000m	ext{ , accelerated motion with decreasing acceleration }t=\dfrac{8+\sqrt{40}}{12}	ext{.}$$

Answer

$$2000m	ext{ , always decelerated motion with increasing deceleration}	ext{.}$$

Answer

Data is insufficient.