Chapter : 1. Motion
Examples on Types of Acceleration
Example : 7
Time-velocity graph of a body is shown in the figure. Find its acceleration in m/s2.
Solution. As it is clear from the figure,
At t = 0 s, v = 20 m/s
At t = 4 s,v = 80 m/s
Acceleration, a =
= 15m/s2.
Example : 8
Time-velocity graph of a particle is shown in figure. Find its instantaneous acceleration at following intervals :
(i) at t = 3s
(ii) at t = 6s
(iii) at t = 9s
Solution. (i) Instantaneous acceleration at t = 3s, is given by
a = slope of line AB = zero
(ii) Instantaneous acceleration at t = 6 s, is given by a = slope of line
BC =
= – 10 m/s2
(iii) Instantaneous acceleration at t = 9 s, is given by a = slope of line CD =
= –50 m/s2
Example : 9
Starting from rest, Deepak paddles his bicycle to attain a velocity of 6 m/s in 30 seconds then he applies brakes so that the velocity of the bicycle comes down to 4 m/s in the next 5 seconds. Calculate the acceleration of the bicycle in both the cases.
Solution. (i) Initial velocity, u = 0, final velocity,
v = 6 m/s, time, t = 30 s
Using the equation v = u + at, we have
substituting the given values of u, v and t in the above equation, we get
a =
= 0.2 m/s2; which is positive acceleration.
(ii) Initial velocity, u = 6 m/s, final velocity, v = 4 m/s, time, t = 5 s, then
= ¬ 0.4 m/s2; which is retardation.
Note :The acceleration of the case (i) is positive and is negative in the case (ii).
Time-velocity graph of a body is shown in the figure. Find its acceleration in m/s2.
Solution. As it is clear from the figure,
At t = 0 s, v = 20 m/s
At t = 4 s,v = 80 m/s
Acceleration, a =
= 15m/s2.Example : 8
Time-velocity graph of a particle is shown in figure. Find its instantaneous acceleration at following intervals :
(i) at t = 3s
(ii) at t = 6s
(iii) at t = 9s
Solution. (i) Instantaneous acceleration at t = 3s, is given by
a = slope of line AB = zero
(ii) Instantaneous acceleration at t = 6 s, is given by a = slope of line
BC =
= – 10 m/s2(iii) Instantaneous acceleration at t = 9 s, is given by a = slope of line CD =
= –50 m/s2Example : 9
Starting from rest, Deepak paddles his bicycle to attain a velocity of 6 m/s in 30 seconds then he applies brakes so that the velocity of the bicycle comes down to 4 m/s in the next 5 seconds. Calculate the acceleration of the bicycle in both the cases.
Solution. (i) Initial velocity, u = 0, final velocity,
v = 6 m/s, time, t = 30 s
Using the equation v = u + at, we have
substituting the given values of u, v and t in the above equation, we get
a =
= 0.2 m/s2; which is positive acceleration.(ii) Initial velocity, u = 6 m/s, final velocity, v = 4 m/s, time, t = 5 s, then
= ¬ 0.4 m/s2; which is retardation. Note :The acceleration of the case (i) is positive and is negative in the case (ii).
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