wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A sprinter starts from rest and accelerates at a steady rate for the first 50m of a 100m race, and then continues at a constant velocity for the second 50m of the race. If the sprinter runs the 100m in a time of 10s, what is his instantaneous velocity when he crosses the finish line?

A
5m/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
10m/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
12m/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
15m/s
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
E
20m/s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D 15m/s
We know the total distance the sprinter covers, and we know the total time. However, since the acceleration isnt uniform, we cant calculate the velocity quite so simply. Rather, we need two equations, one for the first 5 0 meters of the race, and another for the second 5 0 meters. In the first 50 meters, the sprinter accelerates from an initial velocity of v0=0 to a final velocity of v in an amount of time, t1. We can express this relationship using the kinematic equation that leaves out velocity, and then solve for t:
x=x0+12(r+v0)t1
50m=12vt1
t1100mv
In the last 5 0 meters of the race, the sprinter runs with a constant velocity of v , covering a distance of x = 50 m in a time t2, Solving for, t2 we find:
t2=50mv
We know that the total time of the race, t1+t2=10s. With this in mind, we can add the two sprint times together and solve for v :
10s=100mv+50mv=150mv
v=150m10s=15m/s

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Motion Under Constant Acceleration
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon