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 rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m s–2. Calculate the initial thrust (force) of the blast.
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.
You are travelling in a car. The driver suddenly applies the brakes and you are pushed forward. Why does this happen?
Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than that of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.
Find the reading of the spring balance shown in the following figure. The elevator is going up with an acceleration g/10, the pulley and the string are light and the pulley is smooth.
The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall to the earth's surface with a constant velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v?
A force \[\vec{F} = \vec{v} \times \vec{A}\] is exerted on a particle in addition to the force of gravity, where \[\vec{v}\] is the velocity of the particle and \[\vec{A}\] is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?
Find the acceleration of the blocks A and B in the three situations shown in the following figure.
Define linear momentum and state its S.I. unit.
Write the mathematical form of Newton's second law of motion. State the conditions if any.
The correct form of Newton's second law is :
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : Change in momentum of the body.
A pebble is thrown vertically upwards with a speed of 20 m s-1. How high will it be after 2 s? (Take g = 10 m s-2)
State Newton's second law of motion. Is Newton's first law of motion contained in Newton's second law of motion?
A stone is dropped from a cliff 98 m high.
What will be its speed when it strikes the ground?
A metre scale is moving with uniform velocity. This implies ______.
In the previous problem (5.3), the magnitude of the momentum transferred during the hit is ______.
The motion of a particle of mass m is given by x = 0 for t < 0 s, x(t) = A sin 4 pt for 0 < t < (1/4) s (A > o), and x = 0 for t > (1/4) s. Which of the following statements is true?
- The force at t = (1/8) s on the particle is – 16π2 Am.
- The particle is acted upon by on impulse of magnitude 4π2 A m at t = 0 s and t = (1/4) s.
- The particle is not acted upon by any force.
- The particle is not acted upon by a constant force.
- There is no impulse acting on the particle.
