A cart traveling at 0.3 m/s collides with stationary object. After the collision, the cart rebounds in the opposite direction. The same cart again traveling at 0.3 m/s collides with a different stationary object. This time the cart is at rest after the collision. In which collision is the impulse on the cart greater?A. The first collision. B. Cannot be determined without knowing the rebound speed of the first collision. C. The second collision. D. Cannot be determined without knowing the mass of the cart. E. The impulses are the same.

Explanation:

First case

A cart speed is 0.3m/s. i.e the initial velocity is u=0.3m/s

It collide with a stationary body, then after collision the ball rebounds and move in opposite direction. This shows that the ball have a velocity after impulse let say v

Then, impulse is given as the change in linear momentum of a body

Impulse =m∆v

I=m(v-u)

Note, momentum is a vector quantity.

I=m(v--u)

I=m(v+u)

I=m(v+0.3)

I¹=0.3m+mv. Equation 1

Second case

A cart speed is 0.3m/s. i.e the initial velocity is u=0.3m/s

It collide with a stationary body, then after collision the ball is at rest, this show that the final velocity is v=0

Then, impulse is given as the change in linear momentum of a body

Impulse =m∆v

I=m(v-u)

Note, momentum is a vector quantity.

I=m(v--u)

I=m(v+u)

In this case v=0 u=0.3m/s

I=m(0+0.3)

I²=0.3m. Equation 2

If we compare impulse 1 (I¹) to impulse 2 (I²)

Subtract equation 2 from 1

We have, I¹ - I² =0.3m+mv -0.3m

I¹ - I² =mv

I¹ =mv+I²

We notice that the first impulse (I¹) is greater than second impulse (I²) by mv.

The correct answer is A

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y