A car starts from an initial velocity of 10m/s and accelerates at 2.5m/s².how long will it take the car to reach a speed of 40m/s.. How far doea the car travel during this time?
v = Vi + a t
v = 10 + 2.5 t
40 = 10 + 2.5 t
t = 30/2.5
x = vi t + (1/2) a t^2
= 10 t + 1.25 t^2
Well, I always appreciate when cars are in a rush to go somewhere! Let's calculate how long it will take for this speedy car to reach a speed of 40 m/s.
To calculate the time, we can use the formula:
v = u + at
Where:
v = final velocity (40 m/s)
u = initial velocity (10 m/s)
a = acceleration (2.5 m/s²)
t = time
By rearranging the equation, we can solve for t:
t = (v - u) / a
Plugging in the values, we get:
t = (40 - 10) / 2.5
t = 30 / 2.5
t = 12 seconds
So, it will take this car 12 seconds to reach a speed of 40 m/s.
Now, let's find out how far the car travels during this time. We can use another formula:
s = ut + (1/2)at²
Where:
s = distance
u = initial velocity
t = time
a = acceleration
Plugging in the values:
s = (10 * 12) + (1/2 * 2.5 * 12²)
s = 120 + (1/2 * 2.5 * 144)
s = 120 + 180
s = 300 meters
Therefore, this speedy car will travel a distance of 300 meters during the time it takes to reach a speed of 40 m/s.
To find the time it takes for the car to reach a speed of 40 m/s, we can use the formula:
v = u + at
where:
v = final velocity = 40 m/s
u = initial velocity = 10 m/s
a = acceleration = 2.5 m/s²
t = time
Rearranging the formula to solve for time:
t = (v - u) / a
Plugging in the values:
t = (40 - 10) / 2.5
t = 30 / 2.5
t = 12 seconds
So, it will take the car 12 seconds to reach a speed of 40 m/s.
To find the distance the car travels during this time, we can use the formula:
s = ut + 0.5at²
where:
s = distance
u = initial velocity = 10 m/s
t = time taken = 12 seconds
a = acceleration = 2.5 m/s²
Plugging in the values:
s = (10 * 12) + (0.5 * 2.5 * (12)²
s = 120 + (0.5 * 2.5 * 144)
s = 120 + (0.5 * 2.5 * 144)
s = 120 + (0.5 * 360)
s = 120 + 180
s = 300 meters
So, the car will travel a distance of 300 meters during this time.
To find the time it takes for the car to reach a speed of 40 m/s, we can use the equation of motion:
v = u + at
where:
v = final velocity (40 m/s)
u = initial velocity (10 m/s)
a = acceleration (2.5 m/s²)
t = time
Rearranging the equation, we have:
t = (v - u) / a
Substituting the given values, we get:
t = (40 m/s - 10 m/s) / 2.5 m/s²
t = 30 m/s / 2.5 m/s²
t = 12 seconds
Therefore, it will take the car 12 seconds to reach a speed of 40 m/s.
To find the distance traveled during this time, we can use another equation of motion:
s = ut + 0.5at²
where:
s = distance traveled
u = initial velocity (10 m/s)
t = time (12 s)
a = acceleration (2.5 m/s²)
Plugging in the values, we have:
s = (10 m/s)(12 s) + 0.5(2.5 m/s²)(12 s)²
s = 120 m + 0.5(2.5 m/s²)(144 s²)
s = 120 m + 180 m
s = 300 meters
Therefore, the car will travel a distance of 300 meters during the time it takes to reach a speed of 40 m/s.