# Distance traveled from 0 - 100?

If car accelerates from 0 - 100 km/h in 10 seconds and if acceleration is rising at the same rate, how far would a car travel before reaching 100 km/h? So if at 1 second it is at 10 km/h at 2 seconds 20 km/h and so on.. having 1 km/h added with every second.

Update:

Correction, "having 10 km/h added with every second."

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• JJ
Lv 7
4 weeks ago

There's no need for graphs and formulas, this one is a no-brainer:

At 100 kph the car travels about 27.7778 meters per second.

so... 27.7778 meters/sec * 10 sec = 277.778 meters

Since the acceleration was linear, simply cut that in half... 138.889 meters

• Dixon
Lv 7
4 weeks ago

Sketch the time versus velocity, graph and the distance is the area of the triangle.

Convert numbers to common units, eg km and hours.

distance = (1/2)(10/(60 x 60)) x 100

distance = 0.139 km

distance = 139 m

This is also one of the constant acceleration suvat equations,

d = (1/2)(u + v)t

• 4 weeks ago

RE: ". . . and if acceleration is rising at the same rate . . ."

and

RE: ". . . having 10 km/h added with every second."

No, the acceleration is not increasing, the velocity is increasing.

That's what acceleration is, a change in velocity

a = acceleration = 10 km/h/s = 2.7777778 m/s

v0 = initial velocity = 0 km/h = 0.0 m/s

v = final velocity = 100 km/h = 27.777778 m/s

Δx = distance = to be determined

v² = (v0)² + 2aΔx

v² - (v0)² = 2aΔx

[v² - (v0)²] / 2a = Δx

Δx = [v² - (v0)²] / 2a

Δx = [27.78 m/s)² - (0.0 m/s)²] / 2(2.778 m/s²)

Δx = 138.88889 m ≈ 139 m