Newton’s Second Law corrected the old belief that force is needed to maintain motion. This idea came from the philosopher:
Advertisements
Advertisements
Question
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is ______.
Options
136 N
134 N
158 N
68 N
MCQ
Fill in the Blanks
Advertisements
Solution
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is 136 N.
Explanation:
Given, mass = 2 kg
`x(t) = pt + qt^2 + rt^3`
`v = (dx)/(dt) = p + 2qt + 3rt^2`
`a = (dv)/(dt) = 0 + 2q + 6rt`
At t = 2s; a = 2q + 6 × 2 × r
= 2q + 12r
= 2 × 4 + 12 × 5
= 8 + 60
= 68 m/s
Force = F = ma
= 2 × 68
= 136 N
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms–1. How long does the body take to stop?
Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to
- A,
- B along the direction of string. What is the tension in the string in each case?
A person drops a coin. Describe the path of the coin as seen by the person if he is in
- a car moving at constant velocity and
- in a free falling elevator.
In a TV picture tube, electrons are ejected from the cathode with negligible speed and they attain a velocity of 5 × 106 m/s in travelling one centimetre. Assuming straight-line motion, find the constant force exerted on the electrons. The mass of an electron is 9.1 × 10−31 kg.
Both the springs shown in the following figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?
A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg, respectively. Assuming that the magnitudes of acceleration and deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 m/s2.
An empty plastic box of mass m is found to accelerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?
Find the mass M of the hanging block in the following figure that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.
Find the acceleration of the 500 g block in the following figure.
An aeroplane is moving uniformly at a constant height under the action of two forces (i) Upward force (lift) and (ii) Downward force (weight). What is the net force on the aeroplane?
Two bodies A and B of same mass are moving with velocities v and 2v, respectively. Compare their (i) inertia and (ii) momentum.
Prove mathematically F = ma
Which of the following has the largest inertia?
A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is ______.
A woman throws an object of mass 500 g with a speed of 25 ms1.
- What is the impulse imparted to the object?
- If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object?
Figure shows (x, t), (y, t ) diagram of a particle moving in 2-dimensions.
|
|
 (b) |
If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.
Why is catching a slow-moving ball easier than catching a fast-moving ball?
What happens when a car brakes to come to a stop?
