For any arbitrary motion in space, which of the following relations are true
$(a)$ $\left. v _{\text {average }}=(1 / 2) \text { (v }\left(t_{1}\right)+ v \left(t_{2}\right)\right)$
$(b)$ $v _{\text {average }}=\left[ r \left(t_{2}\right)- r \left(t_{1}\right)\right] /\left(t_{2}-t_{1}\right)$
$(c)$ $v (t)= v (0)+ a t$
$(d)$ $r (t)= r (0)+ v (0) t+(1 / 2)$ a $t^{2}$
$(e)$ $a _{\text {merage }}=\left[ v \left(t_{2}\right)- v \left(t_{1}\right)\right] /\left(t_{2}-t_{1}\right)$
(The 'average' stands for average of the quantity over the time interval $t_{1}$ to $t_{2}$ )
For any arbitrary motion in space, which of the following relations are true
$(a)$ $\left. v _{\text {average }}=(1 / 2) \text { (v }\left(t_{1}\right)+ v \left(t_{2}\right)\right)$
$(b)$ $v _{\text {average }}=\left[ r \left(t_{2}\right)- r \left(t_{1}\right)\right] /\left(t_{2}-t_{1}\right)$
$(c)$ $v (t)= v (0)+ a t$
$(d)$ $r (t)= r (0)+ v (0) t+(1 / 2)$ a $t^{2}$
$(e)$ $a _{\text {merage }}=\left[ v \left(t_{2}\right)- v \left(t_{1}\right)\right] /\left(t_{2}-t_{1}\right)$
(The 'average' stands for average of the quantity over the time interval $t_{1}$ to $t_{2}$ )
$(a)$ False: It is given that the motion of the particle is arbitrary. Therefore, the average velocity of the particle cannot be given by this equation.
$(b)$ True: The arbitrary motion of the particle can be represented by this equation.
$(c)$ False: The motion of the particle is arbitrary. The acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of the particle in space.
$(d)$ False: The motion of the particle is arbitrary; acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of particle in space.
$(e)$ True: The arbitrary motion of the particle can be represented by this equation.
Similar Questions
A hiker stands on the edge of a cliff $490\; m$ above the ground and throws a stone horizontally with an initial speed of $15 \;m/ s$. Neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. (Take $g = 9.8 \;m /s^2$ ).
A hiker stands on the edge of a cliff $490\; m$ above the ground and throws a stone horizontally with an initial speed of $15 \;m/ s$. Neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. (Take $g = 9.8 \;m /s^2$ ).
While travelling from one station to another, a car travels $75 \,km$ North, $60\, km$ North-east and $20 \,km $ East. The minimum distance between the two stations is.......$km$
A ball is rolled off along the edge of a horizontal table with velocity $4 m/s$. It hits the ground after time $0.4 \,\,s$. Which of the following are correct?
A ball is rolled off along the edge of a horizontal table with velocity $4 m/s$. It hits the ground after time $0.4 \,\,s$. Which of the following are correct?
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are $(0,2)$. The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are $(0,2)$. The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
A particle is moving along a curve. Then
A particle is moving along a curve. Then