What is the Time to Slide 10m After Falling from a Truck?

[angel1410]

Homework Statement

A box accidentally falls from the back of a truck and hits the ground with a speed of 15m/s[Forward]. It slides along the groud with uniform acceleration for a distance of 45m before coming to rest. Determine the time it takes to slide the last 10m

Homework Equations

v2=v1+a t
displacement=vi x t + 1/2 acceleration x t^2
displacement=v1 +v2 /2 x time

The Attempt at a Solution

 

[PhysicsAdvice]

surely you can give it a try ! :), state the givens you have there

 

[angel1410]

surely you can give it a try ! :), state the givens you have there

Well, i tried with the equation displacement=v1 x time + 1/2 (acceleration) (time)^2
but i am not sure if i am using the right equation and subbing in the variables right.
I subbed in: v1=15m/s acceleration=-2.5m/s^2 displacment=10m v2=0
and I got the answer 11.29m but i am not sure if its right. HELP!

 

[zgozvrm]

Well, i tried with the equation displacement=v1 x time + 1/2 (acceleration) (time)^2
but i am not sure if i am using the right equation and subbing in the variables right.
I subbed in: v1=15m/s acceleration=-2.5m/s^2 displacment=10m v2=0
and I got the answer 11.29m but i am not sure if its right. HELP!

The question is, How much time does it take the box to travel it's last 10m before coming to rest?

The answer you gave is 11.29m.
That's not a quantity of time.


You need to determine how fast the box is moving after it travels 35m, which is when it has 10m left to travel.

Then you can determine how much time it takes to travel from that speed to 0m/s.

 

[paragchitnis]

vf² = vi² + 2ax
0 = 225 -2 x a x 45 ( Box becomes rest finally. So the acceleration is negative )
a = 2.5 m/s² in opposite direction
x = vit + at²/2
35 = 15t - 2.5t²/2
28 = 12t - t²
t = 6 - 2$$\sqrt{2}$$ sec.
similarly,
Total time T = 6sec.
Time taken to cover last 10m = 6 - 6 + 2$$\sqrt{2}$$
$$\approx$$ 2 x 1.41
= 2.82 sec.
Is it correct?

 

[zgozvrm]

Perfect!