Assume that an object moves on a trajectory according to the equations x(t)=t+cost, y(t)=t−sint. Find the magnitude of the acceleration vector.

ddaeeric 2020-11-12 Answered
Assume that an object moves on a trajectory according to the equations x(t)=t+cost,y(t)=tsint. Find the magnitude of the acceleration vector.
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Expert Answer

Latisha Oneil
Answered 2020-11-13 Author has 100 answers
Step 1
An object moves on a trajectory according to the equations
x(t)=t+cost,y(t)=tsint
Differentiating with respect to t, we get
x(t)=1sint,y(t)=1cost
Again differentiating with respect to t, we get
x(t)=cost,y(t)=sint
Step 2
Now, acceleration vector is
a(t)=x(t)i^+y(t)j^
a(t)=i^cost+j^sint
Magnitude of acceleration vector is evaluated as follows.
|a(t)|=(cost)2+(sint)2=cos2t+sin2t=1
Step 3
Result: Magnitude of acceleration vector is 1 unit.
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