2.) A sports car is advertised to be able to stop in a distance of 50m from a speed of 90 km/h. What is its acceleration in m/s^2? How many g's is this (g=9.80 m/s^2)
change the speed to m/s
speed=90km/hr=90,000m/3600 sec solve that.
Vf=0 (stopped)
vf^2=vi^2+2ad solve for a.
How many g's? divide by 9.8
so what do I put into the equation :
vf^2=vi^2+2ad solve for a.
I'm confused on the question how many g's ?
g=9.80 m/s^2 so wouldn't dividing by 9.8 make the how many g's =0 ZERO?
Yes acceleration in m/s^2 /9.81 = number of g s
To find the acceleration of the sports car, we will need to use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
However, in this case, we don't have the time it takes for the car to come to a stop. But we do know the distance it takes to stop, which is given as 50 meters.
To find the time it takes for the car to stop, we can use the formula for distance:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Since the car starts at a speed of 90 km/h and stops at a distance of 50 meters, we can convert the initial velocity to meters per second (m/s) for consistency.
To convert km/h to m/s, multiply by 1000/3600 (since there are 1000 meters in a kilometer and 3600 seconds in an hour):
initial velocity = 90 km/h * (1000 m/km) / (3600 s/h) = 25 m/s
Now, we can rearrange the distance formula to solve for time:
50 = (25 * t) + (1/2 * a * t^2)
Since we are solving for acceleration, we can rewrite the equation as a quadratic equation:
1/2 * a * t^2 + 25t - 50 = 0
To solve for time, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1/2, b = 25, and c = -50.
Using the quadratic formula, we find the two possible values for time. However, we discard the negative value since time cannot be negative in this context.
Once we have the value of time, we can substitute it back into the initial acceleration equation to find the acceleration:
acceleration = (final velocity - initial velocity) / time
In this case, since the car comes to a stop, the final velocity is 0 m/s.
Once we have the acceleration in m/s^2, we can convert it to g's by dividing it by the acceleration due to gravity (g = 9.80 m/s^2).
By following these steps, you should be able to find the acceleration in m/s^2 and then convert it to g's.