 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

A train starts from rest and moves with a constant acceleration for the first 1 km. For the next 3 km, it has a constant velocity and for the last 2 km, it moves with constant retardation to come to rest after a total time of motion of 10 min. Find the maximum velocity and the three time intervals in the three types of motion.


4 years ago

							Suppose the velocity of the train increases from 0 to v in time t1, then moves with constant speed v upto time t2 and finally its velocity decreases from v to 0 between time interval t2 and t.For motion between t=0 and t=t1 let acceleration be \alpha.Then, \alpha = (v-0)/(t1-0)  = v/t1=> t1 = v/\alphaSimilarly, for retardation \beta\beta = (v-0)/(t-t2)  = v/(t-t2)=> t-t2 = v/\beta=> t1+t-t2 = v/\beta + v/\alpha=> t2-t1 = t - v{1/\alpha + 1/\beta}Draw a graph of the motion of the train, from where we can find the displacement of the train.Now, for total displacement S = 1+3+2 = 6 km, and total time taken t=10 min = 1/6 h, we have.S = v.t1/2 + v(t2-t1) + v(t-t2)/2S = v2/2\alpha + v[t- v{1/\alpha + 1/\beta}] + v2/2\betaS/v = v{1/\alpha + 1/\beta}/2 + t - v{1/\alpha + 1/\beta} = t - v{1/\alpha + 1/\beta}/2or, t = S/v + v{1/\alpha + 1/\beta}/2Puutting the values of the variables, the max. velocity attained "v" can be claculated.THANKS

4 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Mechanics

View all Questions »  ### Course Features

• 101 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions