Question

a car travels around a circular path of radius 45m. if the car increases speed at the constant rate of 1.2m/s^2starting from the rest. determine the time needed for it to reach on acceleration of 1.4m/s^2. what is it's speed at this instant

Answer 1

oh... this is non-uniform circular motion.

Answer 2

The net acceleration is sqrt( atan^2 + ac^2)=1.4m/sec^2
atan= tangential acceleration and ac is centripetal acceleration.

atan = 1.2 m/sec^2

ac= v^2/r , v = u+at = 0+ 1.2t
=> ac = 1.44t^2/45 = 0.032t^2

a net = sqrt ( (1.2)^2 + (0.032t^2)^2) = 1.4
squaring on both sides,

1.96 = 1.44 + (1.024*10^-3) t^4

t^4 = (1.96-1.44)*10^3/1.024 = 507.8

=> t = 4.747 seconds.

Answer 3

@kartiksriramk are you sure should have consider the total acceleration ?
I think we should consider tangent acceleration.

Answer 4

@mahmit2012 Well,the question only says at what time will the acceleration be 1.4m/sec^2 and it doesn't particularly mention centripetal acceleration.So I thought it is the net acceleration.

Answer 5

because the centripetal acceleration just keep the vehicle on the road and has no role to increases the velocity .

Answer 6

Yeah but centripetal acceleration itself is a function of the velocity of the vehicle.

Answer 7

yes with quadratic form but when radius keep constant.Ok thank you .

Answer 8

You're welcome.

Answer 9

Oh I forgot the second part. speed at that instant is 1.2*t = 1.2*4.747 = 5.69 m/sec.

Answer 10

i was just about to say but i calculated it

Answer 11

No problem.Did you verify the answer?

Answer 12

ya thnx for the answer

Answer 13

You're welcome.

Answer 14

but anet = 1.4 then how come u did 1.2*t

Answer 15

rate to increase speed related to at=tangent accelaretion v=v0+at*t

Answer 16

if the car increases speed at the constant rate of 1.2m/s^2

Answer 17

Only tangential acceleration contributes to the increase in speed.

Answer 18

got it

Answer 19

shall i post 1 more question