It's gonna crash!

In a crash test, a 1.5 1.5 metric ton vehicle collides a brick wall. The initial velocity of the vehicle is v i = 10 m/s v_{i}=-10\text{ m/s} while its final velocity is v f = 2.6 m/s v_{f}=2.6\text{ m/s} . If the collision lasts for 0.2 0.2 seconds, what is the average force (in Newtons) exerted on the vehicle due to the collision?

Image credit: Wikipedia Brady Holt


The answer is 94500.

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4 solutions

Aditya Raut
Jul 20, 2014

We know that F = m a \overrightarrow F=m \overrightarrow a .

m = 1.5 m= 1.5 ton = 1500 = 1500 kg.

a = v t \overrightarrow a = \frac{\triangle \overrightarrow v}{\triangle t} .

As the velocity changed from 10 m / s -10 m/s to 2.6 m / s 2.6 m/s ,

the value of v = 12.6 \triangle \overrightarrow v = 12.6 .

And t = 0.2 \triangle t = 0.2 as given,

So we get F = m v t = 1500 × 12.6 0.2 = 1500 × 12.6 × 5 = 94500 N F= m \frac{\triangle \overrightarrow v}{\triangle t} = \dfrac{1500 \times 12.6}{0.2} = 1500\times 12.6\times 5 = \boxed{94500} N

👍👌 it was very nice question…

satyam satyam - 6 years, 10 months ago

For those who live in countries that uses the short ton, 1 ton is only equivalent to 907 kg. This will throw off the answer since the question is written using long ton which has a 1 ton to 1016 kg ratio .

Bright Sun - 6 years, 10 months ago

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It says metric ton

Arpit Jain - 6 years, 9 months ago

I thought 1 metric ton was 1000000 kg

Godwin Tom George - 6 years, 8 months ago

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Hee...heee... .

It's bad luck. Never mind, you knew how to solve this problem didn't you?

Muhammad Arifur Rahman - 6 years, 1 month ago
Andrea Gallese
Jul 19, 2014

Due to the impulse theorem p = m v = F m t \triangle p = m \cdot \triangle v = F_m \cdot \triangle t Hence F m = m v t = ( 1.5 1 0 3 k g ) ( 2.6 m / s ( 10 m / s ) ) 0.2 s = 94500 N F_m = \frac{m \cdot \triangle v}{\triangle t}=\frac{(1.5\cdot 10^3 kg)(2.6 m/s -(-10 m/s))}{0.2 s} = \boxed{94500 N}

Vinit Béléy
Sep 28, 2014

v = 2.6 m/s ; u = -10 m/s ; t = 0.2 s

Since v = u + at ; a = 63 m/s2

F = ma = (1.5x1000)kg x 63 m/s2 = 94500 N

Vishal Yash
Aug 29, 2014

we can easily compute acceleration further calculate the force exerted by the vehicle ..........

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