An object accelerates from rest, and after traveling 145 m it has a speed of 420 m/s. What was the acceleration of the object? I am not sure how to calculate acceleration without being given the time directly.

Explanation:

Here,we've been given that,

We've to find the acceleration of the object. By using the third equation of motion,

→ v² - u² = 2as

→ (420)² - (0)² = 2 × a × 145

→ 176400 - 0 = 290a

→ 176400 = 290a

→ 176400 ÷ 290 = a

→ 608.275862 m/s² = a

If you know initial speed and final speed, you can find the average speed.  Then, knowing distance, you can find the time.

KimYurii posted the first answer to this question.  

That answer is well organized, well presented, elegant and correct, and it deserves to be awarded "Brainliest" and several merit badges.

My problem is that I can never remember all the different formulas.  I guess I had to work with so many uvum in all the Physics, Geometry, and Calculus classes that I took, I filled up all the memory slots with formulas, and over the years they all eventually merged into a big glob of goo.  Now, the only formulas I can remember are the ones I had to use as an Electrical Engineer.

When I see this kind of question, I can only remember one or two simple formulas, and I reason it out like this:

Starting speed . . . zero

Ending speed . . . 420 m/s

Formula:  Average speed . . . (1/2)·(0 + 420) = 210 m/s

Distance covered . . . 145 m

Formula: Time taken = (distance) / (average speed) = (145/210) second

(Now you have the time.)

Formula: Distance = (1/2)·(acceleration)·(time²)

145 m = (1/2)·(acceleration)·(145/210 sec)²

Acceleration = 290 m / (145/210 s)²

Acceleration = 608.28 m/s²

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

what is the actual question though?