Exams › NEET › Physics

Equation of motion of a body is \( \frac{\boldsymbol{d v}}{\boldsymbol{d t}}= \) \( 6-3 v, \) where \( v \) is the velocity in \( m s^{-1} \) and \( t \) is the time in second. Assuming particle at rest initially. Then This question has multiple correct options

1. velocity of the body when its acceleration is zero is \( 2 m s^{-1} \)
2. initial acceleration of the body is \( 6 m / s^{2} \)
3. the velocity of the body when the acceleration is half the initial value is \( 1 \mathrm{m} / \mathrm{s} \)
4. the body has a uniform acceleration

Correct answer: initial acceleration of the body is \( 6 m / s^{2} \)

Solution

At the instant the particle starts from rest, v = 0. Substituting into dv/dt = 6 - 3v gives acceleration = 6 m/s², so the initial acceleration statement is correct. The acceleration is not uniform because it depends on v, which changes with time.

Related NEET Physics questions

• A body covers 26,28,30 and 32 meters in \( 10^{t h}, 11^{t h}, 12^{t h} \) and \( 13^{t h} \) seconds respectively. The body starts
• Assertion A body with constant acceleration always moves along a straight line. Reason A body with constant magnitude of acceleration may not speed up.
• A swimmer while jumping into water from a height easily forms a loop in air, if
• The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the velocity of the particle is \( 0.8 m / s \) at \( x=0, \) the velocity of the particle at \( x= \) 1.4 is \( (\text { in } m / s) \)
• Assertion Average velocity of the body may be equal to its instantaneous velocity at all points of time. Reason If a body is having uniform motion in one dimension, then velocity is constant and average velocity can be equal to instantaneous velocity
• An object travels 10 s with uniform acceleration along a straight line path. During this period if the velocity of the object is increased from \( 5 m s^{-1} \) to \( 25 s^{-1}, \) then find the distance travelled by the body?

⚔️ Practice NEET Physics free + battle 1v1 →