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A particle is moving Eastwards with a velocity of 5m/s. In 10s , the velocity changes to 5 m/s Northwards. The average acceleration in this time is
The coordinates of a particle moving in a plane are given by x(t)=acos(pt) and y(t)=b sin(pt) where a,b(<a) and p are positive constants of appropriate dimensions. Then which of the following option is not true
The displacement of a body is given by 2s=gt², where g is a constant. The velocity of the body at any time t is
The position vector r of particle of mass m is given by the following equation:r(t)=αt³î + βt²ĵ where α=(10/3)m/s³, β=5m/s² and m=0.1 kg. At t=1s, which of the following statement is false about the particle?
Correct Answer : d
Explanation: t→=αt3+βt2jˆ ltBrgt velocity, = dr/dt = 3αt^2Iˆ+2βtjˆ
Acceleration, a→=dv/dt
=6αtiˆ+2βjˆ
At t=1s,
(a)Angular momentum Lˆ= r × vrcp
=r × mv
:. L = [10/3(1)3iˆ+5(1)2jˆ]×0.1(10iˆ+10haatj)
=(−5/3kˆ)Nms
(b) v = 3×103×(1)2Iˆ+2×5×1×jˆ
=(10iˆ=10jˆ)ms−1
(c ) Torque τ = r × F
= [10/3(1)^3ahti+5(1)^2jˆ]×(2iˆ+jˆ)
= (10/3iˆ+5jˆ)×(2iˆ+jˆ)
= 10/3kˆ+10(−kˆ)
=(−20/3kˆ)N−m
(d) Force F = ma = 0.1(6×10/3×iˆ+2aht5jˆ)
=(2iˆ+jˆ)N
A particle of mass m moves on the xaxis as follows:it starts from rest at t=0 from the point x=0 and comes to rest at t=1 at the point x=1. No other information is available about its motion at intermediate times(0<t<1). If α denotes the instantaneous acceleration of the particle, then
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