First slide

Instantaneous velocity

Question

A particle moves along the X-axis with its position x given as a function of time t by the equation ${x= -bt+ct}^{2}$ , where b and c are positive constants. At what time, the velocity of the particle will be equal in magnitude and opposite in direction to its initial velocity?

Moderate

A

at t = b/2c
B

at t = 2b/c
C

at t = b/c
D

at t = b/4c

Solution

Comparing with $x = ut + (1 / 2) {at}^{2}$ , we get $u = - b and a = 2 c$ . Using $v = u + at, b = - b + 2 ct$ which gives $t = b / c$

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