Question

The jamaican bobsled team hit the brakes on their sled so that it decelerates at a uniform rate of 0.43 m/s squared how long does it take to stop if it travels 85 m before coming to rest

Answer 1

To calculate the time it takes for the Jamaican bobsled team to come to a stop, we first determine the initial velocity using the kinematic equation and then calculate the time using the initial velocity and deceleration rate.

Step-by-step explanation:

The Jamaican bobsled team decelerates at a uniform rate of 0.43 m/s2 and travels 85 m before coming to rest. To find the time taken to stop, we will use the kinematic equation for uniformly accelerated motion:

v2 = u2 + 2as

Where v is the final velocity, u is the initial velocity, a is the acceleration (or deceleration in our case, and thus negative), and s is the distance covered.

Since the bobsled comes to rest, v = 0, and we need to find u (the initial velocity), which we can then use to calculate the time t using the formula v = u + at. Rearranging the equation to solve for u gives us:

u = sqrt(2as) = sqrt(2 * -0.43 m/s2 * 85 m)

Next, we use the initial velocity u to find the time t:

0 = u + (-0.43)t

t = -u / (-0.43)

This calculation will give us the time the bobsled takes to come to a complete stop.

Answer 2

Time taken, t = 19.86 seconds

Step-by-step explanation:

It is given that,

Deceleration of the sled, a = -0.43 m/s²

We have to find the time it take to stop if it travels 85 m before coming to rest i.e final velocity v = 0. Using third equation of motion as :

`v^2-u^2=2as`

`0-u^2=2* (-0.43\ m/s^2)* 85\ m`

u = 8.54 m/s

The initial velocity of the sled is 8.54 m/s. For finding time taken by the sled to stop can be calculated using second equation of motion as :

`s=ut+(1)/(2)at^2`

`85=8.54t+(1)/(2)* (-0.43)t^2`

`0.215t^2-8.54t+85=0`

On solving the above quadratic equation we get, t = 19.86 seconds. Hence, this is the required solution.