Mechanics> Can the velocity of an object reverse dir...

Can the velocity of an object reverse direction when its acceleration is constant? If so, give an example ; if not, explain why.

Radhika Batra , 10 Years ago

Grade 11

3 Answers

Kevin Nash

Last Activity: 10 Years ago

Yes, the velocity of the object can reverse direction when its acceleration is constant.
For example consider that the velocity of any object at any time t is given as:
v(t) = t – 2.
At At t = 0 sec, the magnitude of velocity is 2m/s and is moving in the forward direction i.e.v (t) = -2. The negative sign here direction of motion, we consider the forward direction to be negative and backward to be positive.
The acceleration of the object is the derivative of v(t) and is;
$a (t) = \frac{dv(t)}{dt}$
$= \frac{d(t-2)}{dt}$
$= 1\ m/\ s^{2}$
At t = 2 the velocity v (t) of the object is:
v (t) = t – 2
= 2 – 2
= 0 m / s
However, the acceleration remains constant:
The acceleration of the object is the derivative of v (t) and is:
$a (t) = \frac{dv(t)}{dt}$
$= \frac{d(t-2)}{dt}$
$= 1\ m/\ s^{2}$
Later as the value of increases and becomes greater than 2 sec , the sign of the velocity changes and becomes positive, that is the object start to move in the backward direction.
At t= 3 sec, the velocity is:
v (t) = 1
While the acceleration remains:
The acceleration of the object is the derivative of v (t) and is:
$a (t) = \frac{dt(t)}{dt}$
$= \frac{d(t-2)}{dt}$
$= 1\ m / s^{2}$

alien

Last Activity: 7 Years ago

suppose a body thrown vertically upwaard with some initial velocity,as it is moving upward with constant force of gravity acting downward producing constant acceleration (9.8 ) which is opposite to direction of velocity .the velocity decreases with passage of time at its highest point its velocity becomes zero and it continue to to move vertically downward.but during whole process force or acceleration due to gravity remaains constant because the force producing it is constant.

Rishi Sharma

Last Activity: 5 Years ago

Dear Student,
Please find below the solution to your problem.

The object can change direction once. For example, take a pen and throw it up in the air. Disregarding drag, there is only one force acting on the pen as it travels. The force due to gravity is constant, and we know that it will accelerate the pen with a constant magnitude of
As the pen travels, it will initially be moving upwards with decreasing velocity. As it reaches its maximum height, it will stop momentarily and then change its direction of motion.
From there on, the velocity will only continue to increase towards the ground unless its acceleration changes and becomes a non-constant value.
It can reverse its direction and after collision with a relatively giant sized body like earth, it can reverse its direction again, possibly a few times. If you have an object travelling up with acceleration g downwards, the body’s direction reverses after reaching the top. Then upon hitting ground again, the body reverses it direction again. The collision does not have to be elastic, but an average type of collision with earth reverses direction of the body. We therefore often observe a ball bouncing up and down many times before it settles down. A point must be made though. During the short periods of time during which the collision with the ground is actually happening, the acceleration is different. :

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