Two carts are set in motion at t 0 on a frictionless track n a physics laborator

Question

Two carts are set in motion at t 0 on a frictionless track n a physics laboratory. The first cart is launched rrom an initial po x . 19.6 cm with a constant velocity nf 4 40i cm/s ton or x = 17,0 c with an initial velocity or 12 cm s and a oon ant a celeration c 3.75 cm ge, The second cart is launched for (a) What are the times for which the two certs have equal speeds? earlier time 202 ater tirne b What ane the spasds af the carts at thosa timas? earlier time 440 Cm/s )What are the locations and times at which the carts pass carlier timc arlier position later time later position each ather? ) What is the differanca hetwcen what is asked in parts (a) and (c) of this prablem with regard to tha times you found? This sever has not been80ed yet Need Help?Hoad Submit AngrSav Prss Practike Another Version

Explanation / Answer

(A) speed of 2nd car is constant.

for first car, v = v0 + a t

v = 12 - 3.75t = 4.40

t = 2.03 sec  

and after that when first car is moving in negative direction that means v = - 4.40

12 - 3.75 t = - 4.40

t = 4.37 sec

Ans: 2.03, 4.37 sec

2. Speed will be 4.40 cm/s.

3. car will pass when their position will be same.

x1 = 17 + (12 t) + (-3.75 t^2/ 2)

x1 = 17 + 12 t - 1.875t^2

and x2 = 19.6 + 4.40 t

x1 = x2

1.875 t^2 - 7.6 t + 2.6 = 0

t = 0.38 sec Or 3.68 sec  

Earlier time : 0.38 s

position: 1.66 cm

later time : 3.68 s

later position: 16.2 cm

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