Home
Class 11
PHYSICS
A cyclist riding with a speed of 27 km h...

A cyclist riding with a speed of `27 km h ^(-1).` As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of `0.5 ms^(-1)` every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

Text Solution

Verified by Experts

`v = 27 kmh ^(-1) = ( 27 xx 5)/( 18) = 7. 5 ms ^(-1) , r = 80 m `
We know that, centripetal acceleration, `a _(c) = (v ^(2))/( r ) = (( 7.5) ^(2))/( 80) = 0. 7 m//s ^(2).`
Suppose that the cyclist applies breaks at the point A of the circular turn. So retardation produced due to breaks `(a _(T))` will act opposite to the velocity (v) . So `a_(T) = - 0. 5 m//s ^(2).`

Total acceleration is given by
`a = sqrt (a _(c)^(2) + a _(r) ^(2)) = sqrt ((0. 7) ^(2) + (- 0 .5 ) ^(2) ) = sqrt ( 0. 49 + 0. 25 ) = sqrt ( 0. 74) = 0. 86 m//s ^(2).`
If ` theta ` is the angle between net acceleration and velocity of cyclist, then
`tan theta = (a _(c))/( a _(T)) = ( 0. 7)/( 0. 5) = 1. 4 or theta = 54 ^(@) 28,`
Promotional Banner

Similar Questions

Explore conceptually related problems

A cyclist is riding with a speed of 27 km//h . As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m//s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?

A cyclist going at a speed of 24 km h^-1 ,takes a turn of 6.70 m radius .Find the inclination of his cycle to vertical.

A cyclist starats from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in the figure.If he maintains constant speed of 10 ms^(-1) , what is his acceleration at point R in magnitude and direction?

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^-1 to 3.5 m s^-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?

A particle executing circular motion of radius 5 m and linear speed of 3 ms^-1 which is increasing at the rate of 2 m s^-2 .What is the acceleration of the particle?

Figure shows a conducting rod PQ in contact with metal rails RP and SQ, which are 0.25 m apart in a uniform magnetic field of flux density 0.4T acting perpendicular to the plane of the paper. Ends R and S are connected through a 5 Omega resistance. What is the emf when the rod moves to the right with a velocity of 5ms^(-1) ? What is the magnitude and direction of the current through the 5 Omega resistance? If the rod PQ moves to the left with the same speed, what will be the new current and its direction?

A cyclist speeding at 18 km h^-1 on a level road makes a sharp circular turn of radius 3 m without reducing the speed. The coefficient of static friction between the tyres and the road is 0.1 will the cyclist slip while taking the turn?

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h^-1 in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period Tof the bus service and with what speed (assumed constant) do the buses ply on the road?