# A driver in a car traveling at a speed of 21.8 m/s sees a car 101 m away on the road. How long will it take for the car to uniformly decelerate to a complete stop in exactly 99 m?

Since we know that velocity is uniformly decelerating, we can take the average velocity:

Hope this helps!

Cheers

By signing up, you agree to our Terms of Service and Privacy Policy

To find the time it takes for the car to decelerate to a complete stop, we can use the equation of motion for uniformly decelerated motion:

[ v^2 = u^2 + 2a s ]

Where:

- ( v ) is the final velocity (0 m/s, as the car comes to a stop),
- ( u ) is the initial velocity (21.8 m/s),
- ( a ) is the acceleration (which is negative since the car is decelerating),
- ( s ) is the displacement (99 m, the distance over which the car decelerates).

Rearranging the equation to solve for acceleration (( a )), we get:

[ a = \frac{{v^2 - u^2}}{{2s}} ]

Substituting the given values, we have:

[ a = \frac{{0^2 - (21.8)^2}}{{2 \times 99}} ]

[ a = \frac{{-475.24}}{{198}} ]

[ a ≈ -2.4 , \text{m/s}^2 ]

Now, we can use the equation of motion for uniformly accelerated motion to find the time (( t )) it takes for the car to decelerate to a stop:

[ v = u + at ]

Substituting the known values:

[ 0 = 21.8 - 2.4t ]

Solving for ( t ):

[ 2.4t = 21.8 ]

[ t = \frac{{21.8}}{{2.4}} ]

[ t ≈ 9.083 , \text{s} ]

Therefore, it will take approximately 9.083 seconds for the car to uniformly decelerate to a complete stop over a distance of 99 meters.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #64 KJ# to # 180 KJ# over #t in [0, 12 s]#. What is the average speed of the object?
- An object is at rest at #(1 ,3 ,9 )# and constantly accelerates at a rate of #7/4# #ms^-2# as it moves to point B. If point B is at #(2 ,5 ,6 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- In the time that it takes one car to travel 93 km, a second car travels 111 km. If the average speed of the second car is 12 km/h faster than the speed of the first car, what is the speed of each car?
- An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #640 KJ# to # 160 KJ# over #t in [0, 12 s]#. What is the average speed of the object?
- An object's velocity is given by #v(t) = (2t^2 -t +2 , sint )#. What is the object's rate and direction of acceleration at #t=3 #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7