A car with an initial velocity of 8 m/s experiences a constant acceleration for 3 sec, after which the velocity is 17 m/s.
a) What was the acceleration?
b) How far did the car travel during that time interval?
Please help!! ASAP
a = (17-8)/3 = 3 m/s^2
s = vt + a/2 t^2
a) Well, let me tell you, this car sure knows how to accelerate! To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
So, in this case, the final velocity is 17 m/s, the initial velocity is 8 m/s, and the time is 3 seconds. Plugging those values in, the formula becomes:
acceleration = (17 m/s - 8 m/s) / 3 s
Simplifying this calculation, we find that the acceleration is 3 m/s².
b) Now, let's calculate how far the car traveled during that time interval. To do that, we can use another handy formula called the displacement formula:
displacement = initial velocity * time + (1/2) * acceleration * time²
Plugging in the known values, we get:
displacement = 8 m/s * 3 s + (1/2) * 3 m/s² * (3 s)²
Calculating further, we find that the displacement of the car is 46.5 meters.
So, the car had an acceleration of 3 m/s² and traveled 46.5 meters during that time interval. Keep driving, my friend!
a) To find the acceleration, we can use the equation:
v = u + at
Where:
- v is the final velocity (17 m/s),
- u is the initial velocity (8 m/s),
- a is the acceleration, and
- t is the time (3 sec).
Plugging in the values, we have:
17 = 8 + a * 3
Simplifying the equation:
17 - 8 = 3a
9 = 3a
Dividing both sides by 3:
a = 3 m/s²
Therefore, the acceleration of the car is 3 m/s².
b) To find the distance traveled by the car during the time interval, we can use the equation:
s = ut + (1/2)at²
Where:
- s is the distance traveled,
- u is the initial velocity (8 m/s),
- t is the time (3 sec), and
- a is the acceleration (3 m/s²).
Plugging in the values, we have:
s = 8 * 3 + (1/2) * 3 * (3)²
Simplifying the equation:
s = 24 + (1/2) * 3 * 9
s = 24 + (1/2) * 27
s = 24 + 13.5
s = 37.5 meters
Therefore, the car traveled a distance of 37.5 meters during the time interval.
Sure! Let's break down the problem into two parts:
a) To find the acceleration, we can use the formula: final velocity (v) = initial velocity (u) + (acceleration (a) × time (t))
Given:
Initial velocity (u) = 8 m/s
Final velocity (v) = 17 m/s
Time (t) = 3 seconds
Using the formula, we can rearrange it to solve for acceleration:
a = (v - u) / t
a = (17 - 8) / 3
a = 9 / 3
a = 3 m/s²
Therefore, the acceleration of the car is 3 m/s².
b) To find the distance traveled by the car during the time interval, we can use the formula: distance (s) = initial velocity (u) × time (t) + (1/2) × acceleration (a) × time (t)²
Given:
Initial velocity (u) = 8 m/s
Acceleration (a) = 3 m/s²
Time (t) = 3 seconds
Using the formula, we substitute the values:
s = (8 × 3) + (1/2) × 3 × (3)²
s = 24 + (1/2) × 3 × 9
s = 24 + (1/2) × 27
s = 24 + 13.5
s = 37.5 meters
Therefore, the car traveled a distance of 37.5 meters during that time interval.
I hope this helps! Let me know if you have any further questions.