Question

The driver of a car sets the cruise control and ties the steering wheel so that the car travels at a uniform speed of in a circle with a diameter of 120 m. a) Through what angular distance does the car move in 4.00 min? b) What linear distance does it travel in this time?

Answer 1

Answer

given,                                  

diameter of the circle = 120 m

time  =4 min = 4 × 60 = 240 s

linear velocity be = 15 m/s

we know                      

v = r ω                          

ω =$\dfrac{v}{r}$

ω =$\dfrac{15}{60}$

ω = 0.25 rad/s

angular distance in time 4 min

d = ω t                                      

d = 0.25 × 240                          

d = 60 radian              

b) linear distance          

d = s × t                  

d = 15 × 240

d = 3600 m

Answer 2

Answer:

(a) Angular distance is 4v m

(b) Linear distance is 240 v m

Solution:

As per the question:

Let the uniform speed of the car be 'v' m/s

Diameter of the car, D = 120 m

Radius of the car, r = 60 m

Time, t = 4.00 min = 240 s

Now,

(a) The angular speed of the car is given by:

$\omega = \frac{v}{R} = \frac{v}{60}$ rad/s

Now, the angular displacement is given by:

$\theta = \omega\times t$

$\theta = \frac{v}{60}\times 240 = 4v$ m

(b) The linear distance, d is given by:

d = vt = 240v m