The result is -15.625 m/s².
Acceleration signifies the alteration of velocity over a specified duration. It can be calculated with this formula:
Where:
vf = final velocity
vi = initial velocity
t = time
Let’s examine the information provided in your query:
Initially, the vehicle was traveling at 25 m/s before coming to a halt. Thus, it was in motion and subsequently ceased moving, indicating that the final velocity is 0 m/s.
However, we notice that the problem does not provide a time value. We need to determine the time taken from when it was in motion to when it reached the traffic light located 20 m away.
The time can be calculated using the kinematics equation:
We derive the equation by substituting the known values first.
The duration from when it was in motion until it stopped is 1.6s. Now we can utilize this in our acceleration calculation.
It is important to note that the acceleration is negative, indicating the vehicle slowed down.
Refer to the diagram below.
Ignoring air resistance, use gravitational acceleration g = 9.8 m/s².
The pole vaulter drops with an initial vertical speed u = 0.
At impact with the pad, velocity v satisfies:
v² = 2 × (9.8 m/s²) × (4.2 m) = 82.32 (m/s)²
v = 9.037 m/s
As the pad compresses by 0.5 m to bring the vaulter to rest,
let the average acceleration (deceleration) be a m/s². Then:
0 = (9.037 m/s)² + 2 × a × 0.5 m
Solving for a gives:
a = - 82.32 / (2 × 0.5) = -82 m/s²
Thus, the deceleration magnitude is 82 m/s².
Answer:
7.166 hours = 430 minutes.
Explanation:
As both trains are approaching each other on the same track, their relative speed is the sum of their individual speeds. Hence, the time until they intersect (and inevitably collide) is determined by how long it takes for speeds of 65 mph and 55 mph to cover the total distance of 860 miles. One train will cover part of the distance, while the other will cover the remainder. To calculate the required time, we can apply the formula:
1 hour ---> 120 miles
X ----> 860 miles; hence X = (860 miles * 1 hour)/120 miles = 43/6 hours = 7.16666 hours. To convert this into minutes, recall that 1 hour equals 60 minutes; therefore, 43/6 hours * 60 minutes/hour = 430 minutes.
For motion in a circle.
Centripetal acceleration is calculated as mv²/r = mω²r
where v represents linear velocity, r equals radius which is diameter/2 equating to 1/2 or 0.5m
. Here, m is the mass of the object, which is 175g or 0.175kg.
The angular speed, ω, is derived from Angle covered / time
= 2 revolutions per 1 second
= 2 * 2π radians for each second
= 4π radians per second
Thus, Centripetal Acceleration = mω²r = 0.175*(4π)² * 0.5. Utilize a calculator
≈13.817 m/s²
. The acceleration's magnitude is approximately 13.817 m/s² and it is oriented towards the center of the circular path.
The tension in the string equates to m*a
= 0.175*13.817
= 2.418 N
