Question

A ball is thrown vertically upward, ignoring the air resistance, which one of the following plots represents the velocity time plot for the period the ball remains in air?

(A)
 

(B)
 

(C)
 

Answer 1

- Hint: On neglecting the air resistance, the only force now acting on the ball after it is thrown will be the gravitational force and since it is a rectilinear motion thus for drawing its velocity time graphs.

Formula used-
v = u +at
Where v = is the velocity of ball at time t
u = is the initial velocity with which it is thrown.
a = acceleration of the ball.
t = is the time at which we want to know the velocity.

Complete step-by-step solution -

Considering the upward direction of motion as positive
Let u be the initial speed with which the ball is thrown
Then, the final velocity after time t is given by
v = u +at
As we know that the gravitational force is acting vertically downward,
Therefore a = -g
Substituting the value of acceleration in the above equation, we get
v = u-gt
The above equation resembles with the equation of straight line with negative slope i.e. y=mx+c
Hence, the graph will have a straight line with a negative slope of g and an intercept of u.
Hence, the correct option is “A”

Note- The velocity of the ball will decrease as the gravitational force is in the opposite direction of motion then it will reach to zero, then after it will start accelerating in the direction of gravitational force(downward) i.e. negative direction but magnitude will increase. This formula of motion v= u + at is only applicable when the acceleration is constant like here gravitation acceleration for all objects (g) is equal to the 9.8 meters per second square.