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

[werson tan]

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

 

[azizlwl]

First equation, ut=0
Second equation, ut=15.5(1)
Both are wrong. Check again the formula.

 

[gneill]

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.