Question

A particle has an initial velocity of `3hat"i" + 4hat"j"` and an acceleration of `0.4hat"i" + 0.3hat"j"`. Its speed after 10 s is ______.

Options

• `7sqrt2` units

• 7 units

• 8.5 units

• 10 units

Answer 1

A particle has an initial velocity of `3hat"i" + 4hat"j"` and an acceleration of `0.4hat"i" + 0.3hat"j"`. Its speed after 10 s is `bb(7sqrt2)` units.

Explanation:

Given `vec"u" = 3hat"t" + 4hat"j",  vec"a"= 0.4hat"i" +0.3hat"j"`, t = 10s

From 1st equation of motion.

a = `("v"-"u")/"t"`          ∴ v = u + at

⇒ v = `(0.4hat"i" +0.3hat"j")xx10+(3hat"i"+4hat"j")`

⇒ `4hat"i"+3hat"j"+3hat"j"+4hat"j"`

⇒ v = `7hat"i"+7hat"j"`

⇒ `|vec"v"| = sqrt(7^2+7^2)`

= 7`sqrt2` unit.