Two particles are moving along a straight line starting beginning from x(0) = 0

Question

Two particles are moving along a straight line starting beginning from x(0) = 0 with a velocity of v(0) = 10 at time t = 0. Both the particles begin to decelerate. The magnitude of acceleration of the first particle is directly proportional to the time, t and that of the second particle is directly proportional to the speed of the particle. (a) At time t = 2 which particle has the higher velocity? (b) Which particle comes to rest (zero velocity) first and at what time does this occur? Assume the constants of proportionality to be 1. [

Explanation / Answer

for the 1st particle

deceleration = Kt

k =1

deceleration = t

v = u -at

v = 10 - t^2

at t = 2

v = 10 - 4

v = 6 m/s

for body 2

deceleration = Kv

k =1

a = v

v = u - at

v = 10 - vt

v(1+t) = 10

v = 10/(1+t)

at t = 2

v = 10/3

v = 3.333 m/s

lets finfd the time when v becomes zero for both

for 1st

10 - t^2 = 0

t = 3.16 s

for 2nd

0 = 10/(1+t)

so this will take infinite time

so the 1st body comes to rest earlier than the 2nd one

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