Question

At any instant of time acceleration and velocity of a particle are given by vec a=hat i+hat jr vec v=6 hat i+8hat j then rate of change of speed at the same instant will be

Answer 1

The rate of change of speed at that instant = 1.4 m/s

Explanation:

In case of motion in a straight line, the rate of change of speed = magnitude of acceleration.

Here, there is no confirmation if the motion is rectilinear.

At any instant, velocity of particle = v→ = 6i^ + 8j^

vx = x component of velocity = 6

vy = x component of velocity = 8

Acceleration of the particle = a→ = i^ + j^

x and y component of acceleration = ax = ay = 1

Speed at any instant = v = √vx² + vy²  

v² = vx² + vy²  

Differentiating with respect to t, we get: 2v dv/dt = 2vx dvx/dt + 2vy dvy/dt  

v dv/dt = vxax + vyay where dv/dt is the rate of change of speed.

 √6² + 8² dv/dt = 6*1 + 8*1

  √100 dv/dt = 14

   dv/dt = 14/10

   dv/dt = 1.4 m/s