Question

Can cars stop on a dime? Calculate the acceleration of a 1400 kg car if it can stop from 35 km/h on a dime (diameter= 1.7 cm) how many g’s is this?

Answer 1

Answer:

The acceleration of the cart is 283.54g

Explanation:

It is given that,

Initial speed of the car, u = 35 km/h = 9.72 m/s

Finally, it stops, v = 0

Diameter of the dime, d = 1.7 cm

Let a is the acceleration of the car. Using third equation of motion to find it as :

$v^2-u^2=2ad$

$-u^2=2ad$

$a=\dfrac{-u^2}{2d}$

$a=-\dfrac{(9.72)^2}{2\times 1.7\times 10^{-2}}$

$a=-2778.77\ m/s^2$

So, the acceleration of the car is $2778.77\ m/s^2$ and it is decelerating.

Since, $g=9.8\ m/s^2$

So, $a=\dfrac{2778.77}{9.8}=283.54\ g$

So, the acceleration of the cart is 283.54g. Hence, this is the required solution.

Answer 2

Based on this calculation, the acceleration of this car is equal to 283.55g.

Given the following data:

• Initial velocity = 35 km/h

• Mass of car = 1400 kg.

• Distance = 1.7 cm.

Conversion:

• Initial velocity = 35 km/h to m/s = $\frac{35 \times 1000}{60 \times 60}$ = 9.72 m/s.

• Distance = 1.7 cm to m = $\frac{1.7}{100}$ = 0.017 meter.

Scientific data:

• Acceleration due to gravity (g) = 9.8 $m/s^2$

How to calculate the car's acceleration.

In order to calculate the acceleration of this car, we would apply the third equation of motion.

Mathematically, the third equation of motion is given by this formula:

$V^2 = U^2 + 2aS$

Where:

• V is the final velocity.

• U is the initial velocity.

• a is the acceleration.

• S is the distance covered.

Note: The final velocity of the car is equal to zero (0) when it comes to a stop.

Substituting the given parameters into the formula, we have;

$0^2 = 9.72^2 - 2a(0.017)\\\\0.034a = 94.4784\\\\a=\frac{94.4784}{0.034}$

Acceleration, a = 2,778.78 $m/s^2$.

In terms of g:

$Acceleration = \frac{2778.78}{9.8}$

Acceleration, a = 283.55g.

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