A car start from rest an is then accelerated uniformly to a velocity of 100.8km/h.A brake is applied in 4sec.find
1.its acceleration
2.its retardation
v = at
a = (100.8 km/hr)/(4s) = 25.2 (km/hr)/s
no idea what #2 is
To find the answers, we need to use the basic equations of motion. These equations relate displacement, velocity, acceleration, and time. Here's how we can find the answers step by step:
1. Finding the acceleration:
First, we need to convert the final velocity from km/h to m/s. We can do this by dividing it by 3.6 since 1 km/h is equal to 1 m/s divided by 3.6.
Final velocity = 100.8 km/h = (100.8 * 1000) m/3600 s = 28 m/s
The initial velocity of the car is 0 m/s since it starts from rest. We also know that the time taken to reach this velocity is 4 seconds.
We can use the equation: v = u + at, where:
v = final velocity (28 m/s)
u = initial velocity (0 m/s)
a = acceleration (to be found)
t = time (4 seconds)
Rearranging the equation to solve for acceleration (a):
a = (v - u)/t
Plugging in the values, we get:
a = (28 - 0) m/s / 4 s = 7 m/s²
Therefore, the acceleration of the car is 7 m/s².
2. Finding the retardation (deceleration):
As per the given question, a brake is applied to decelerate the car. Retardation is just the negative of acceleration.
Retardation = -acceleration = -7 m/s²
Therefore, the retardation of the car is -7 m/s².
Note: The negative sign indicates that the car is slowing down (decelerating).
1. Well, isn't that car quite the ambitious one! First, it goes from rest to a velocity of 100.8 km/h. To find its acceleration, we need to use the equation:
acceleration = change in velocity / time taken.
The change in velocity can be calculated as follows:
change in velocity = final velocity - initial velocity
Now, let's convert the final velocity from km/h to m/s for the sake of consistency. One km/h is equal to 0.2777778 m/s (approximately).
Final velocity in m/s = 100.8 km/h * 0.2777778 m/s per km/h
So, the final velocity in m/s is approximately 28.0 m/s.
Since the car started from rest, the initial velocity is 0 m/s.
To find the acceleration, we plug these values into the equation:
acceleration = (28.0 m/s - 0 m/s) / 4 s
Therefore, the acceleration of the car is approximately 7.0 m/s².
2. Ah, the brake comes into play. To find the retardation (or deceleration), we can use the same equation as before:
retardation = change in velocity / time taken.
This time, the change in velocity will be the final velocity minus the initial velocity.
We know the final velocity was 0 m/s since the car comes to a stop, and the initial velocity was 28.0 m/s (as we found earlier). The time taken is given as 4 seconds.
Plugging these values into the equation, we get:
retardation = (0 m/s - 28.0 m/s) / 4 s
Thus, the retardation (or deceleration) of the car is approximately -7.0 m/s². Remember the negative sign indicates that it's slowing down, not speeding up. Be careful out there, don't brake too hard!
To find the car's acceleration, we can use the formula:
\[ v = u + at \]
where:
v = final velocity (100.8 km/h)
u = initial velocity (0 km/h, as it starts from rest)
t = time taken to reach the final velocity (t = 4 sec)
Rearranging the formula to solve for acceleration (a):
\[ a = \frac{{v - u}}{{t}} \]
Let's substitute the values:
\[ a = \frac{{100.8 - 0}}{{4}} \]
Simplifying the equation:
\[ a = 25.2 \, \text{km/h}^2 \]
Therefore, the car's acceleration is 25.2 km/h².
To find the car's retardation, we need to convert the final velocity to m/s, as the acceleration due to braking is generally measured in m/s².
1 km/h = 0.27778 m/s
\[ 100.8 \, \text{km/h} \times 0.27778 = 28 \, \text{m/s} \]
Now, we can use the formula:
\[ v = u + at \]
where:
v = final velocity (0 m/s, as the car comes to rest)
u = initial velocity (28 m/s, as it starts braking from 100.8 km/h)
t = time taken to come to rest (t = 4 sec)
Rearranging the formula to solve for retardation (a):
\[ a = \frac{{v - u}}{{t}} \]
Let's substitute the values:
\[ a = \frac{{0 - 28}}{{4}} \]
Simplifying the equation:
\[ a = -7 \, \text{m/s}^2 \]
Therefore, the car's retardation is -7 m/s².