Question

Position as a function of time find time when velocity is perpendicular to acceleration

Answer 1

What is an example when velocity is perpendicular to acceleration?

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Projectile motion: 



The acceleration is always downward. At the highest point, the velocity becomes perpendicular to the acceleration.

Orbital Motion:



Earth's velocity  is perpendicular to acceleration (always towards the sun) at the points where the earth is closest to the sun (winter solstice) and farthest from the sun (summer solstice).

Cyclotron motion:



The acceleration due to a uniform magnetic field is given by a⃗ =q(v⃗ ×B⃗ )/ma→=q(v→×B→)/m. This is always perpendicular to v⃗ v→.