Finding Time and Velocity for a Motorcycle Accelerating at 1.6m/s^2

In summary, the problem involves a motorcycle accelerating at 1.6 m/s^2 and reaching a velocity of 20 m/s over a distance of 50 m. Using the equation s= ut +1/2(a)(t^2), the initial velocity can be found to be 15.5 m/s and the time elapsed is 6.56 seconds. There was a mistake in the attempt at a solution, as the value of t was replaced with "1" in the second equation, resulting in an incorrect answer. It is important to keep all relevant digits when doing calculations to avoid rounding errors.
  • #1
werson tan
183
1

Homework Statement


A motorcycels accelerates at 1.6m/s^2 to reach a velocity of 20m/s of distance 50m . Determine the initial velocity and time elapsed .

Homework Equations

The Attempt at a Solution


to find the velocity , i have 2(1.6)(50) = (20^2)- (u^2) , u = 15.5m/s
but i have problem of finding the time ,
why i can't use the eq of s= ut +1/2(a)(t^2) ,
50 = 0+1/2(1.6)(t^2) , t= 8s ,
50 = 15.5(1) +1/2(1.6)(t^2) , t= 6.56s
the given time = 2.8s
 
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  • #2
First equation, ut=0
Second equation, ut=15.5(1)
Both are wrong. Check again the formula.
 
  • #3
werson tan said:
to find the velocity , i have 2(1.6)(50) = (20^2)- (u^2) , u = 15.5m/s
but i have problem of finding the time ,
why i can't use the eq of s= ut +1/2(a)(t^2) ,
50 = 0+1/2(1.6)(t^2) , t= 8s ,
50 = 15.5(1) +1/2(1.6)(t^2) , t= 6.56s
the given time = 2.8s

You have chosen the correct equation but you are misapplying it. Your second version is closer, as you've correctly used the 15.5 m/s initial velocity, but for some reason you've replaced the t that multiplies it with a "1". Leave the t there. You should end up with a quadratic equation in t.

You might also want to keep a few more decimal places in the value of u when you do additional calculations with it. Otherwise rounding errors can creep into your significant figures as you proceed. Only round values at the end for presentation.
 

1. How can I calculate time and velocity?

To calculate time and velocity, you can use the formula v = d/t, where v is velocity, d is distance, and t is time. Rearrange the formula to solve for t by dividing d by v.

2. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity shows the object's velocity at a particular point.

3. How does acceleration affect time and velocity?

Acceleration is the rate of change of velocity over time. So, the longer an object accelerates, the more time it takes for it to reach a certain velocity. Additionally, a greater acceleration will result in a higher velocity in the same amount of time.

4. Can time and velocity be negative?

Yes, time and velocity can be negative in certain situations. For example, if an object is moving in the opposite direction of a chosen positive direction, its velocity will be negative. Similarly, if an object is slowing down, its acceleration will be negative.

5. How can I use time and velocity to predict an object's future position?

To predict an object's future position, you can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. This formula assumes that the object maintains a constant velocity and does not accelerate or decelerate. If the object is accelerating, you will need to use a different formula, such as d = v0t + 1/2at2, where v0 is the initial velocity and a is the acceleration.

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